Here are some instances of the Fourfold Negation from the Buddhavacana, which does not systematically appear fully fleshed out at all times, but appear contextually, much like the Twelve Nidānas are not exhaustively explored in every single instance of paṭiccasamuppāda-explanation:

Then the naked ascetic Kassapa said to the Blessed One: “We do not wish to ask Master Gotama much.”

“Then ask what you want, Kassapa.”

“How is it, Master Gotama: is suffering created by oneself?”

“Not so, Kassapa,” the Blessed One said.

“Then, Master Gotama, is suffering created by another?”

“Not so, Kassapa,” the Blessed One said.

“How is it then, Master Gotama: is suffering created both by oneself and by another?”

“Not so, Kassapa,” the Blessed One said.

“Then, Master Gotama, has suffering arisen fortuitously, being created neither by oneself nor by another?”

“Not so, Kassapa,” the Blessed One said.

“How is it then, Master Gotama: is there no suffering?”

“It is not that there is no suffering, Kassapa; there is suffering.”

“Then is it that Master Gotama does not know and see suffering?”

“It is not that I do not know and see suffering, Kassapa. I know suffering, I see suffering.”

“Whether you are asked: ‘How is it, Master Gotama: is suffering created by oneself?’ or ‘Is it created by another?’ or ‘Is it created by both?’ or ‘Is it created by neither?’ in each case you say: ‘Not so, Kassapa.’ When you are asked: ‘How is it then, Master Gotama: is there no suffering?’ you say: ‘It is not that there is no suffering, Kassapa; there is suffering.’ When asked: ‘Then is it that Master Gotama does not know and see suffering?’ you say: ‘It is not that I do not know and see suffering, Kassapa. I know suffering, I see suffering.’ Venerable sir, let the Blessed One explain suffering to me. Let the Blessed One teach me about suffering.”

“Kassapa, if one thinks, ‘The one who acts is the same as the one who experiences the result,’ then one asserts with reference to one existing from the beginning: ‘Suffering is created by oneself.’ When one asserts thus, this amounts to eternalism. But, Kassapa, if one thinks, ‘The one who acts is one, the one who experiences the result is another,’ then one asserts with reference to one stricken by feeling: ‘Suffering is created by another.’ When one asserts thus, this amounts to annihilationism. Without veering towards either of these extremes, the Tathagata teaches the Dhamma by the middle:

[here follows an explanation of Dependant Origination]

(SN 12.17)

This instance lacks the third negation (X and not-X), because it is collapsed into the first and second negations:

“Thus this way of regarding things and the notion ‘I am’ have not vanished in him. As ‘I am’ has not vanished, there takes place a descent of the five faculties—of the eye faculty, the ear faculty, the nose faculty, the tongue faculty, the body faculty. There is, bhikkhus, the mind, there are mental phenomena, there is the element of ignorance. When the uninstructed worldling is contacted by a feeling born of ignorance-contact, ‘I am’ occurs to him; ‘I am this’ occurs to him; ‘I will be’ and ‘I will not be,’ and ‘I will consist of form’ and ‘I will be formless,’ and ‘I will be percipient’ and ‘I will be nonpercipient’ and ‘I will be neither percipient nor nonpercipient’—these occur to him.

“The five faculties remain right there, bhikkhus, but in regard to them the instructed noble disciple abandons ignorance and arouses true knowledge. With the fading away of ignorance and the arising of true knowledge, ‘I am’ does not occur to him; ‘I am this’ does not occur to him; ‘I will be’ and ‘I will not be,’ and ‘I will consist of form’ and ‘I will be formless,’ and ‘I will be percipient’ and ‘I will be nonpercipient’ and ‘I will be neither percipient nor nonpercipient’—these do not occur to him."

(SN 22.47)

There are, monks, some ascetics and Brahmins who are Finitists and Infinitists, and who proclaim the finitude and infinitude of the world on four grounds. What are they?

Here a certain ascetic or Brahmin has by means of effort attained to such a state of concentration that he dwells perceiving the world as infinitude. He thinks: "This world is finite and bounded [...]."
[...]
And what is the second way? [...] He dwells perceiving the world as infinite. He thinks: "This world is infinite and unbounded [...]."
[...]
And what is the third way? [...] He dwells perceiving the world as finite up-and-down, and infinite across. He thinks: "This world is finite and infinite [...]."
[...]
And what is the fourth case? Here a certain ascetic or Brahmin is a logician, a reasoner. Hammering it out by reason, he argues: "This world is neither finite nor infinite [...]."

(DN 1, 2.16-21, Brahmajālasutta, Wrong views 9-12

Here we have an instance of the Fourfold Negation applied to the nature of the knowledge of the Tathāgata. He appears to draw a distinction between "knowing" and "directly knowing":

The Blessed One said this:

“Bhikkhus, in this world with its devas, Māra, and Brahmā, among this population with its ascetics and brahmins, its devas and humans, whatever is seen, heard, sensed, cognized, reached, sought after, examined by the mind—that I know.

“Bhikkhus, in this world with its devas, Māra, and Brahmā, among this population with its ascetics and brahmins, its devas and humans, whatever is seen, heard, sensed, cognized, reached, sought after, examined by the mind—that I have directly known. It has been known by the Tathāgata, but in the Tathāgata it has not been established. (An alternate translation here reads: "but the Tathagata hasn't taken a stance on it")

“Bhikkhus, if I were to say, ‘In this world with its devas … whatever is seen, heard, sensed, cognized, reached, sought after, examined by the mind—that I do not know,’ that would be a falsehood on my part.

6“Bhikkhus, if I were to say, ‘In this world with its devas … whatever is seen, heard, sensed, cognized, reached, sought after, examined by the mind—that I both know and do not know,’ that too would be just the same.

7“Bhikkhus, if I were to say, ‘In this world with its devas … whatever is seen, heard, sensed, cognized, reached, sought after, examined by the mind—that I neither know nor do not know,’ that would be a fault on my part.

(AN 4.24)

In this instance the Fourfold Negation is specified by the Buddha as used to dismiss flawed questions that are irrelevant to the Dhamma:

“These speculative views have been left undeclared by the Blessed One, set aside and rejected by him, namely: ‘the world is eternal’ and ‘the world is not eternal’; ‘the world is finite’ and ‘the world is infinite’; ‘the soul is the same as the body’ and ‘the soul is one thing and the body another’; and ‘after death a Tathāgata exists’ and ‘after death a Tathāgata does not exist’ and ‘after death a Tathāgata both exists and does not exist’ and ‘after death a Tathāgata neither exists nor does not exist.’ The Blessed One does not declare these to me, and I do not approve of and accept the fact that he does not declare these to me, so I shall go to the Blessed One and ask him the meaning of this. If he declares to me either ‘the world is eternal’ or ‘the world is not eternal’…or ‘after death a Tathāgata neither exists nor does not exist,’ then I will lead the holy life under him; if he does not declare these to me, then I will abandon the training and return to the low life.”
[...]
“Why have I left that undeclared? Because it is unbeneficial, it does not belong to the fundamentals of the holy life, it does not lead to disenchantment, to dispassion, to cessation, to peace, to direct knowledge, to enlightenment, to Nibbāna. That is why I have left it undeclared."

(MN 63)

This instance is interesting because it appears that the Buddha may actually be criticizing a) the Fourfold Negation itself, or b) the misapplication of the negations:

'What is the fourth way? Here, an ascetic or Brahmin is dull and stupid. Because of his dullness and stupidity, when he is questioned he resorts to evasive statements and wriggles like an eel:

"If you ask me whether there is another world. But I don't say so. And I don't say otherwise. And I don't say it is not, and I don't not say it is not."

"Is there no other world?..."

"Is there both another world and no other world?...

"Is there neither another world nor no other world?..."

"Are there spontaneously-born beings?..."

"Are there not...?"

"Both...?

"Neither...?"

"Does the Tathagata exist after death? Does he not exist after death? Does he both exist and not exist after death? Does he neither exist nor not exist after death?..."

"If I thought so, I would say so...I don't say so...I don't say it is not."

This is the fourth case.'

(DN 1, 2.27, Brahmajālasutta, Wrong view 16, "Eel-wriggling")

Last edited by Coëmgenu on Wed Jan 11, 2017 1:12 am, edited 1 time in total.

世尊在靈山會上拈華示眾眾皆默然唯迦葉破顏微笑世尊云The Lord dwelt at the Vulture Peak with the assembly and plucked a flower as a teaching. The myriad totality were silent, save for Kāśyapa, whose face cracked in a faint smile. The Lord spoke. 吾有正法眼藏涅槃妙心實相無相微妙法門不立文字教外別傳付囑摩訶迦葉。I have the treasure of the true dharma eye, I have nirvāṇa as wondrous citta, I know signless dharmatā, the subtle dharma-gate, which is not standing on written word, which is external to scriptures, which is a special dispensation, which is entrusted to Mahākāśyapa.नस्वातोनापिपरतोनद्वाभ्यांनाप्यहेतुतः

piotr wrote:Why [X; not-X; X and not-X; not-(X or not-X)] is called "The Fourfold Negation"? It obviously doesn't negate a proposition in four ways.

Its called the "Four, or Fourfold, Negation(s)", but it is also called the "Four Positions" (Tetralemma).

It is given the name because these four positions are almost always either negated or not answered by the Buddha, and if they are negated, there generally follows an explanation of dependent origination.

Substitute X for "persistence of the Tathāgata (after death)", which occurs in a MN 63, and we get this

1. Position: There is a persistence of the Tathāgata, or X. Answer: Negation ("This is not declared[...]")
2. Position: There is no persistence of the Tathāgata, or not-X. Answer: Negation ("This is not declared[...]")
3. Position: There is and is not persistence of the Tathāgata, or X and not-X. Answer: Negation.
4. Position: There is neither persistence nor non-persistence of the Tathāgata, or not-(X or not-X), Answer: Negation

5. Explanation of dependent origination or "the way of the middle" as it is sometimes called in these instances.

I can think of four possible reasons as to why this formation occurs and is followed by a paṭiccasamuppāda-explanation:

a) The Tathāgata, in these instances, is finished discussing flawed or useless questions, and would rather teach the questioner something more useful.

b) The capacity of the questioner is flawed in such a way that any answer in any way would only result in the cultivation of further wrong-views.

c) The Tathāgata (or other subject matter in question) cannot be hypostatized (conceptualizing thought does not apply).

d) The Tathāgata actually does answer the question, the answer as to X (or, for instance, the persistence of the Tathāgata after death) is somehow realized through cultivating understanding of paṭiccasamuppāda.

Last edited by Coëmgenu on Thu Jan 12, 2017 12:58 am, edited 2 times in total.

世尊在靈山會上拈華示眾眾皆默然唯迦葉破顏微笑世尊云The Lord dwelt at the Vulture Peak with the assembly and plucked a flower as a teaching. The myriad totality were silent, save for Kāśyapa, whose face cracked in a faint smile. The Lord spoke. 吾有正法眼藏涅槃妙心實相無相微妙法門不立文字教外別傳付囑摩訶迦葉。I have the treasure of the true dharma eye, I have nirvāṇa as wondrous citta, I know signless dharmatā, the subtle dharma-gate, which is not standing on written word, which is external to scriptures, which is a special dispensation, which is entrusted to Mahākāśyapa.नस्वातोनापिपरतोनद्वाभ्यांनाप्यहेतुतः

It is just (what was regarded as) a complete consideration of the possible truth status of a proposition.

It has precedence in India (Catuṣkoṭi), but it only systematically appears as specifically negations in Buddhist discourse, as far as I know anyways. I could well be wrong.

世尊在靈山會上拈華示眾眾皆默然唯迦葉破顏微笑世尊云The Lord dwelt at the Vulture Peak with the assembly and plucked a flower as a teaching. The myriad totality were silent, save for Kāśyapa, whose face cracked in a faint smile. The Lord spoke. 吾有正法眼藏涅槃妙心實相無相微妙法門不立文字教外別傳付囑摩訶迦葉。I have the treasure of the true dharma eye, I have nirvāṇa as wondrous citta, I know signless dharmatā, the subtle dharma-gate, which is not standing on written word, which is external to scriptures, which is a special dispensation, which is entrusted to Mahākāśyapa.नस्वातोनापिपरतोनद्वाभ्यांनाप्यहेतुतः

I can think of four possible reasons as to why this formation occurs and is followed by a paṭiccasamuppāda-explanation:

a) The Tathāgata, in these instances, is finished discussing flawed or useless questions, and would rather teach the questioner something more useful.

Probably not.

b) The capacity of the questioner is flawed in such a way that any answer in any way would only result in the cultivation of further wrong-views.

What is flawed is the question itself because the question is imputing 'self' & 'death' onto the Tathagata, which does not pertain.

c) The Tathāgata (or other subject matter in question) cannot be hypostatized (conceptualizing thought does not apply).

The issue is imputing selfhood. Dependent origination is given as the explanation per the literal definition of 'jati' ('birth') as the conceiving (sañjāti) & reification (abhinibbatti) of "beings" (sattānaṃ) based on the appearance/look (pātubhāvo) of the aggregates & mental enslavement (paṭilābho) to the sense objects.

d) The Tathāgata actually does answer the question, the answer as to X (or, for instance, the persistence of the Tathāgata after death) is somehow realized through cultivating understanding of paṭiccasamuppāda.

Understanding of paṭiccasamuppāda results in the understanding a Tathagata is not subject to birth, aging & death thus questions about the after death of a Tathagata do not apply.

1. Position: There is a persistence of the Tathāgata, or X. Answer: Negation ("This is not declared[...]")

This is the view of eternalism, believing a "being" (satta) continues after death, as Mara believed in SN 5.10.

2. Position: There is no persistence of the Tathāgata, or not-X. Answer: Negation ("This is not declared[...]")

This is the view of nihilism, in believing a "being" (satta) perishes at death, as Yamaka believed in SN 22.85.

3. Position: There is and is not persistence of the Tathāgata, or X and not-X. Answer: Negation.

This is combining what Mara & Yamaka believed.

4. Position: There is neither persistence nor non-persistence of the Tathāgata, or not-(X or not-X), Answer: Negation

This sounds similar to what Nagarjuna would possibly believe.

5. Explanation of dependent origination or "the way of the middle" as it is sometimes called in these instances.

Yes. Dependent origination explains how the view of "beings" (satta) is "born" (jati) or hypostatized. When dependent origination is discerned, there is no more "birth" of the view of "beings" (satta) therefore no "person" imagined as the Tathagata let alone a Tathagata that experiences "death". Arahants do not experience either birth or death because their minds are void of conceiving (mannati) 'self'.

"'He has been stilled where the currents of construing do not flow. And when the currents of construing do not flow, he is said to be a sage at peace.' Thus was it said. With reference to what was it said? 'I am' is a construing. 'I am this' is a construing. 'I shall be' is a construing. 'I shall not be'... 'I shall be possessed of form'... 'I shall not be possessed of form'... 'I shall be percipient'... 'I shall not be percipient'... 'I shall be neither percipient nor non-percipient' is a construing. Construing is a disease, construing is a cancer, construing is an arrow. By going beyond all construing, he is said to be a sage at peace.

"Furthermore, a sage at peace is not born, does not age, does not die, is unagitated, and is free from longing. He has nothing whereby he would be born. Not being born, will he age? Not aging, will he die? Not dying, will he be agitated? Not being agitated, for what will he long? It was in reference to this that it was said, 'He has been stilled where the currents of construing do not flow. And when the currents of construing do not flow, he is said to be a sage at peace.'

MN 140

You are free to provide evidence from the Pali that what was posted above is lies & misinformation.

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@SN 12.17 - The questions asked imply the existence of a self. Suffering arises dependent on other things than those listed by the questioners. Asking such questions means the questioner did not understand the doctrine of dependent origination and therefore, the Buddha tells him to study it again so that he understands it and therefore, also understand the answer to his questions.

@SN 22.47 - The Buddha explains how there is no self so ideas such as "I am this" or "I am not this" do not arise.

@AN 4.24 - There is no 4 fold negation here. The Buddha simply explains that he knows those things and that it would be wrong to say " I do not know" or "I neither know or not know" etc. because he does know.

@MN 63 - As you said, it is used to dismiss flawed questions.

This instance is interesting because it appears that the Buddha may actually be criticizing a) the Fourfold Negation itself, or b) the misapplication of the negations:

It is the misapplication of negations. While it does apply to questions regarding the self or the arahant after death, it does not apply to other things. For example you can not apply it to form. Form that is impermanent exists, so Buddha simply says that form exist.

You'll have a better chance finding a moderate rebel in Ildib than finding a buddhist who ever changed his views. Views are there to be clung to. They are there to be defended with all one's might. Whatever clinging one will removed in regards to sense pleasures by practicing the path - that should be compensated with increased clinging to views. This is the fundamental balance of the noble 8thfold path. The yin and yang.
----------Consciousness and no-self explained in drawings:link
How stream entry is achieved. Mahasi / Zen understanding vs Sutta understanding: link

* The Eye sees a picture with shape and colour. The eye-consciousness gives it volume and depth. The feeler aggregate draws on memories to create a negative or positive emotion.
* The Skin is bruised. The skin-consciousness senses a harsh contact. The feeler aggregate draws on memories to give it a negative emotion. The physical pain is an expression of the feeler aggregate.
* Mother is killed in car crash. The mind-consciousness senses the loss of a volitional object. The feeler aggregate associated the object with safety and security that no longer here.

If the "one" is a fabrication who suffers? Into which account does one credit the suffering?

The sensory input triggers a thought. As per the Abhidhamma every thought passes through 18 stages. The consciousness uses name-form associations to label the thoughts i.e. The round shape is called "a circle".

The cognizer gives it meaning i.e. biscuit. The feeler triggers signals. The consciousness again interprets the feeling name-form it as "delicious". The cognizer congnizes and the feeler feels. Although the sum of sensing, perceiving, feeling and cognising appear as one unit.

All that exists is flat-data. The aggregate interprets the flat data and gives it meaning and depth. The suffering is also manufactured this way.

The Sutta Pitaka's and the ancient Pali commentaries read like a legal document. The purpose is to unambiguously emphasise the "self" is a manufactured aggregate.

The four-fold negation is used here to be emphatic the "one" as one perceive really do not exist.

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Unsurpassed is the Lord’s way of teaching the Dhamma concerning one’s proper moral conduct. One should be honest and faithful, without deception, chatter, hinting or belittling, not always ready to add gain to gain, but with the sense-doors guarded, moderate in food, a promoter of peace, observant, active and strenuous in effort, a meditator, mindful, with proper conversation, steady-going, resolute and sensible, not hankering after sense pleasures, but mindful and prudent. This is the unsurpassed teaching concerning a person’s proper ethical conduct. - Sampasādanīya, Dīgha Nikāya 28

About those questions about what happens to an arahant after death, it is quite simply to see why they are wrong. They all imply that there is/was a self. While in reality there was never a self to begin with. There is no arahant that dies. There are just the 5 aggregates that cease without reminder. There was never an arahant (witch implies a self) to begin with, just the 5 aggregates that exist and make up that being. There is nobody there to experience the death. There never was anybody there to experience anything. Just the 5 aggregates that used to exist and now do not exist anymore.

Another way to understand it better: There is not a person that experiences suffering. There is just suffering that arises. This person or self that supposedly experiences things was always just an invention, just an opinion. Same as Freud "super ego" and other ideas of his that people laugh about now. Just an invention, just an opinion that has arisen. It is not a self that perishes, there never was a self to begin with.

Another way to understand it even more better: Imagine a car parking sensor. There are 2 elements. The physical parking sensor and the "sensor sights" or the thing the sensor perceives. This sensor perception then triggers the beep-beep to start. In the case of a being, there are 3 elements. There is the eye, eye sights and a 3rd one - eye consciousness. Then these things trigger volition, feelings etc. to arise like the parking sensor triggers the beep-beep. There is not a self that sees the eye sights. There is just eye consciousness/ear consciousness/mind consciousness/nose consciousness etc.

A puthijhana understands consciousness like that son of a fisherman that asked buddha about consciousness than transmigrates from one body to the other. He imagines consciousness something like a ball that sees all these eye sights, ear sights etc. While in reality consciousness is something like a sheet that is put on these things. This is not the most correct way to explain it but it is an attempt. For more on consciousness:

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You'll have a better chance finding a moderate rebel in Ildib than finding a buddhist who ever changed his views. Views are there to be clung to. They are there to be defended with all one's might. Whatever clinging one will removed in regards to sense pleasures by practicing the path - that should be compensated with increased clinging to views. This is the fundamental balance of the noble 8thfold path. The yin and yang.
----------Consciousness and no-self explained in drawings:link
How stream entry is achieved. Mahasi / Zen understanding vs Sutta understanding: link

“Kassapa, if one thinks, ‘The one who acts is the same as the one who experiences the result,’ then one asserts with reference to one existing from the beginning: ‘Suffering is created by oneself.’ When one asserts thus, this amounts to eternalism. But, Kassapa, if one thinks, ‘The one who acts is one, the one who experiences the result is another,’ then one asserts with reference to one stricken by feeling: ‘Suffering is created by another.’ When one asserts thus, this amounts to annihilationism. Without veering towards either of these extremes, the Tathagata teaches the Dhamma by the middle:

Again, the above appears to point to dependent origination in order to negate the self-views that are eternalism & annihilationism. This again supports the view that dependent origination is explaining the birth of self-views ('self' & 'other') rather than explaining reincarnation. In short, the creator of suffering is the element (dhatu) of ignorance.